Algebra 2 Properties of Real Numbers

In this lecture, you'll learn about the subsets of the real numbers, like the natural numbers and fractions. There are a few essential properties you need to know about Real Numbers. Firstly, a real number corresponds to a point on the number line. Since there are infinitely many points on a line, there are also infinitely many real numbers. Secondly, real numbers are either rational or irrational; rational numbers can be expressed as a fraction while irrational cannot. For example, pi is an irrational number. Thirdly, the relationship between the various types of real numbers can be expressed using Venn diagram. Lastly, real numbers are commutative and associative under addition, and multiplication have additive and multiplicative identities and inverses, and satisfy the distributive property.

The first property of real numbers that allows you to do those calculations is the commutative property of real numbers.

This property allows you to re - arrange your terms in any way without affecting the final result.

The second property is the associative property of real numbers. This property allows you to group of terms together without changing the final result of the calculation.

[1/9] was multiplied by its multiplicative inverse. What is the final result? What is the multiplicative inverse of [1/9]?

Any number, variable, or expression multiplied by its multiplicative inverse is always going to result in 1.

Since a*[1/a] = 1, then the multiplicative inverse of [1/9] is 9.

A student in Mr. Inca's Algebra II class stated the following The identity property of addition is one because when you add one, you're not really changing the original quantity that much. Is this student correct in his assertion about the identity property of addition? Explain.

The student is incorrect. By definition, the identity property of addition does not change the original quantity. Zero is the one and only identity property of addition.

When discussing the identity property of multiplication in class, Mr. Flores stated the following: The identity property of multiplication is 0 because when you multiply something by nothing, you should still get what you started with back. Is Mr. Flores correct about the identity property of multiplication? If not, then what is it?

Mr. Flores is incorrect. He's trying to decieve his class by making them believe that 0 is the identity property of multiplication. While 0 is the identity property of addition, 1 is the identity property of multiplication.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Properties of Real Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.